There are several mechanisms that are related to the fluctuation phenomena in QCM. The purpose of our research is to analyze the sensitiveness and the influence of different sorts of noise on detector declaration. Our experiments are performed on detectors with a sorption bed of polypyrrole which is suited for sensing of H2O vapour. Based on these experiments, we conclude that 1/f noise caused by quartz internal clash and adoption-desorption ( generation-recombination ) noise from analyzed gas cause the chief constituents of the mensural noise spectral denseness. The adoption-desorption noise power depends on the physical and chemical parametric quantities of the analyzed gas and it is relative to the gas denseness. The adsorption-desorption dynamicss is described by Kolmogorov ‘s equation and is compared with the Wolkenstein and Langmuir equations.
Keywords- vitreous silica crystal microbalance ; Kolmogorov equations ; adsorption-desorption noise ; noise spectrometry
Quartz crystal microbalance ( QCM ) represents a high-sensitivity detector for sensing of chemical substances, and is widely utilized as a consequence of its robust nature, handiness and low-cost interface electronicsA [ 1 ]. The bosom of the detector is AT-cut quartz crystal whose electrodes are covered by sorption beds with affinity to the molecules of the detected affair. Since the resonance frequence of quartz crystal depends on the entire oscillatory mass, the rule of QCM is a frequence displacement caused by the add-on of occluded affair ( molecules of the detected mass ) to the electrodes or its remotion from them. Therefore, the sensitiveness depends on the stableness of the oscillator and the truth and stableness of the devices mensurating the parametric quantities of the vitreous silica resonating chamber. The selectivity is given by the pick of the stuff of the sorption bed.
Analysiss of noise measurings represent the attack of pull outing more selective response from chemical detectors, such as resistive [ 2-6 ] and surface acoustic moving ridge [ 7 ] detectors. Experimental consequences showed that the noise spectral denseness of the detector ‘s opposition fluctuations is modified by exposure to different gases every bit good as by exposure to different concentration of gases [ 5 ]. Therefore, noise spectrometry might be extremely utile for bettering gas detectors selectivity if both theoretical theoretical accounts and equal detection devices can be developed [ 3 ]. Gomri et al [ 4 ] proposed a theoretical account of adsorption-desorption noise in metal oxide gas detectors, based on the free negatron denseness fluctuation produced by the gas surface assimilation. Using this theoretical account for imitating the O chemosorption – induced noise, they found that the part of O adsorption-desorption noise to the noise spectra is a Lorentzian constituent holding a corner frequence and low frequence magnitude which are particulars of the adsorbed gas.
The paper trades with an experimental survey how soaking up of detected gas molecules affects frequency fluctuations of QCM, and presents the theoretical account of adsorptionaˆ‘desorption noise which is devoted on the footing of Kolmogorov equation for interaction between two reservoirs.
Two standard attacks of QCM measuring exist, viz. the active method and the inactive method. In the first one, the vitreous silica crystal is a portion of a wideband oscillator circuit whose frequence is controlled by the crystal belongingss [ 1 ] and is measured by a frequence counter with a declaration of 1A Hz, 0.1A Hz or 0.01A Hz. Some research workers [ 6 ] usage a mention oscillator to avoid ambient effects. In that instance, a counter measures the frequence difference between the end product signal of the detector based oscillator, and the end product signal of the mention vitreous silica based oscillator. In the inactive attack, a QCM receives a frequence which is determined by an external beginning [ 2 ]. Therefore, the frequence displacement and the displacement in bandwidth ( relative to dissipation ) can be obtained by entering the complex entree around a resonance frequence and fitting resonance curves to the entree spectra.
In order to analyze a little frequence fluctuation of QCM, the active method was modified to mensurate instantaneous frequence of QCM. The strategy of our measuring apparatus is shown in Fig. 1. The measurement apparatus consists of a quartz crystal with deposited sorption beds ( mensurating oscillator ) and a quartz crystal without sorption beds ( mention oscillator ). These crystals are driven by two independent oscillator circuits that regulate frequence of each vitreous silica crystal at the lower limit electric resistance which corresponds to consecutive resonance. The frequence difference a?†f between these two oscillators is a consequence of mixer process and low-pass filtering. This signal is led to an input of a data-acquisition card ( NI 5124 ) which triggers on the rise-edges of the end product signal and shops the corresponding times at which the instantaneous frequence is estimated by own-written package.
The experiments were performed on detectors with a thin sorption bed of polypyrrole ( PPY ) which is a stuff suitable for building of QCM humidness detectors. The alteration of comparative humidness from 0A % RH to 25A % RH causes a alteration of resonating frequence ( a?†f ) in the scope 50aˆ‘150 Hz. Sensor parametric quantities ( e.g. sensitiveness, dynamic belongingss, clip stableness of response ) depend non merely on the composing but even on the manner of deposition of the sorption bed. Therefore, PPY was deposited utilizing Matrix Assisted Pulsed Laser Evaporation ( MAPLE ).
This engineering [ 12-16 ] is a optical maser deposition method supplying a soft mechanism for organic bed deposition. In MAPLE, a frozen stage consisting of a dilute solution of a high-molecular weight compound ( basic stuff ) in a low- molecular-weight dissolver ( matrix ) is used as the optical maser mark. Deposition takes topographic point after the impact of a optical maser pulsation with the surface of the frozen mark. In an optimum instance, the energy of the optical maser pulsation is wholly absorbed by the matrix, ensuing in a strong local addition of temperature. The matrix molecules transfer their kinetic energy of thermic gesture to the molecules of basic stuff. Hence the molecules of basic stuff are transferred to the substrate “ automatically ”, with neither photolytic nor pyrolytic harm.
The advantages of MAPLE in comparing with conventional methods can be summarized as follows: ( a ) theA thickness of the prepared beds can be merely controlled by puting optical maser fluence and the figure of pulsations. Therefore, consistent readying of thin beds holding thicknesses of the order of 10s of nanometres is possible. ( B ) The prepared beds are porous ( i.e. they have a high surface/volume ratio ), so they are suited for detector applications. ( degree Celsius ) “ Sandwich ” constructions can be fabricated unmoved in one measure by altering marks during the deposition. ( vitamin D ) The consequence of the optical maser pulsation is strongly limited in clip and localized in infinite, hence there is a possibility to make assorted forms by Matrix-Assisted Pulsed Laser Evaporation – Direct Write method.
The beginning mark for MAPLE was prepared from 5 wt. % H2O solution of polypyrrole ( Mw=10000 ) doped with dodecyl sulfonic acid – specific electrical conduction of the solution: I? = 10-40 S cma?’1 ( Sigma Aldrich ). This solution was stirred and homogenized by an supersonic device. Subsequently, it was frozen to a?’196 A°C in the tubular mold utilizing liquid N. The prepared mark was inserted into the deposition chamber and placed on the revolving shaft of the mark holder. The holder was at the same time cooled by liquid N. Uniform extirpation of the stuff from the mark surface was achieved by changeless rotary motion during the deposition procedure. The deposition chamber was evacuated by a turbomolecular pump to a residuary force per unit area of 5a?™10a?’ 3 Pa. The force per unit area in the chamber did non transcend 3A Pa during the deposition procedure ( a background gas was non used ).
The depositions were carried out utilizing Nd: YAG optical maser ( Quantel ), runing at the 4th harmonic frequence ( wavelength 266 nanometer ). The Neodymium: YAG optical maser was used in a pulse manner with a 10 Hz repeat rate. The fluence F of the optical maser radiation was set by an attenuator to be F = 0.4 J cma?’2. The substrate – vitreous silica crystal ( without any surface cover ) was placed at a distance of 60 millimeter. The deposited PPY beds have a thicknesses runing from 80 to 400 nanometers.
Figure 2 shows good understanding between comparative humidness measurings, where a commercial available humidness detector ( FH A646-1, ALBHORN ) and a QCM with deposited polypyrrole were used. RH addition from 25 % to 85 % causes a rise of frequence difference a?†f between mensurating oscillator and mention oscillator for about 400 Hz.
Consequences and Fluctuation Mechanisms in QCM
Several mechanisms related to fluctuation phenomena exist in QCM. The cardinal noise includes thermic noise, 1/fA noise due to the quantum fluctuation and phonon sprinkling by defects, adoption-desorption noise from the analyzed gas, thermo-mechanical noise, temperature fluctuation noise, and electronic oscillator noise. The mechanisms can be separated into two groups ; the first one is related to the vitreous silica crystal and its electrical circuit, while the 2nd one is related to the adsorption-desorption processes on a sorbent bed. Experimental consequences shown in Fig.A 3 reveal that the 1/f noise, thermic noise and generation-recombination ( adsorption desorption ) noise seem to be the chief noise constituents. FigureA 3 besides shows the spectral denseness of QCM has a higher incline of 1/f noise portion and a higher value of GR constituent in comparing to the noise spectrum of the measuring system, which was determined on the footing of the measuring of frequence difference fluctuation utilizing two indistinguishable vitreous silica crystals without active bed.
There are assorted theoretical accounts and mechanisms that could be responsible for the ascertained noise, particularly for 1/f noise ( e.g. [ 8-11 ] ) ; nevertheless, this paper focuses merely on fluctuation mechanisms connected with chemical procedures on the active bed of QCM.
Figure 4 illustrates how the spectral denseness SI”f ( degree Fahrenheit ) of the frequence difference fluctuations is affected by the absorption/desorption of H2O molecules by the QCM detector. When the RH additions, the 1/f noise constituent alterations insignificantly while the G-R constituent perceptibly increases with a rise of RH value. The writers of this paper suppose that thermic noise constituent and 1/f noise constituent are chiefly associated with quartz crystal belongingss represented by its tantamount circuit, while generationaˆ‘recombination noise consequences from adsorptionaˆ‘desorption procedures which are present on the active bed of the QCM detector. Further, it can be assumed that a displacement of G-R noise is caused by increased flux denseness between the sorbent bed of QCM and the ambient environment. Sing these interactions between the two reservoirs, a theoretical account of adsorption-desorption noise could be formulated on the footing of Kolmogorov equation.
This subdivision presents a theoretical account of surface assimilation desorption noise related to RH concentration. The value of the adoption-desorption noise depends on the physical and chemical parametric quantities of the analyzed gas. Adsorption-desorption dynamicss is described by the Kolmogorov equation and compared with the Langmuir and Wolkenstein equations.
5.1. Kolmogorov equation
A proposed theoretical account of adsorption-desorption noise is based on interaction between two reservoirs:
analyzed gas with concentration Ns, temperature T and partial force per unit area P,
detector sorbent surface with entire surface denseness of sites for the surface assimilation of analyzed gas N0, with surface denseness of sites occupied by analyzed gas molecules Nt
5.1.1. Passage chance strengths
The theoretical account supposes that the system is: ( I ) Markowian, ( two ) A near equilibrium, and ( three ) generation-recombination processes may take topographic point between these two reservoirs. The random procedure of the surface site is assumed to hold two provinces and to be stationary with a changeless passage chance denseness Aµij defined by
( 1 )
where Palestine Islamic Jihad devotes the passage chance at clip s from the iaˆ‘state to the jaˆ‘state at clip t. Figure 5a shows the theoretical account of adsorption-desorption procedure on the quartz crystal sorbent bed. Desorption corresponds to molecule emanation from sorbent, i.e. coevals of free atom, and the procedure of surface assimilation corresponds to recombination. Therefore, the procedure is similar to generation-recombination inA semiconducting materials. The passage chance denseness for emanation and gaining control is schematically shown in Fig.A 5b, where Aµ01 is the passage chance denseness for the molecule emanation and Aµ10 forA gaining control. There are two physical measures: the characteristic clip I„c for a molecule to be captured on the surface site which is reciprocally relative to the passage chance denseness Aµ10
Aµ10A =A 1/ I„cA ( 2 )
and the characteristic clip I„e for molecule emanation from the surface site which is reciprocally relative to the passage chance denseness Aµ01
Aµ01A =A 1/ I„eA ( 3 )
The chances pijA ( T ) of the passage from the province I into the province jA areA found by work outing the Kolmogorov differential equations
( 4 )
for I, J = 0, A 1, with the conditions pii ( 0 ) =1, Palestine Islamic Jihad ( 0 ) =0, forA iA a‰ A J. In thermodynamic equilibrium, the statistics, that the surface site is free or occupied by a molecule, is described by the absolute chance distributions I 0 and I 1. These 1s are given by work outing the Kolmogorov equation [ 17 ] for stationary province in the signifier
( 5 )
where ( 6 )
( 7 )
The absolute chance distributions I 0 and I 1 are similar to the Fermi – Dirac statistics.
5.1.2. Kinetic equation
Kinetic equation depicting surface denseness of adsorbed molecules follows from ( 5 ) in the signifier
( 8 )
( 9 )
where Aµ00, A Aµ11 are densenesss that the system is prevailing in the province 0 or 1 severally. With Aµ01A =A CNA n1A forA coevals, Aµ10A =A CNA nA for recombination and CN as coefficient of gaining control,
. ( 10 )
The surface denseness of adsorbed molecules is relative to the coefficient of gaining control CN, concentration of adsorbed molecules n, sensor surface denseness of sites N0 and the effectual concentration of occupied sites n1.
5.2. Langmuir surface assimilation dynamicss
The rate of formation of the monolayers can be written as [ 18 ]
( 11 )
where I?A =A N/N0A, CA denotes concentration of analyzed gas molecules, Ka and kd are the rate invariables for surface assimilation and desorption procedures, severally. Integration of ( 11 ) and permutations kobs = Ka + kilobit and K ‘ = CA / ( C + kd/ka ) lead to
( 12 )
If the fractional coverage I? is measured as a map of clip T, coefficients kobs and k ‘ can be determined by suiting of ( 11 ) on the experimental information.
5.3. Wolkenstein surface assimilation dynamicss
The rate of formation of monolayers is [ 3, A 4 ]
( 13 )
( 14 )
( 15 )
where I is the chance that a molecule nearing an surface assimilation Centre will be fixed on the detector surface, p – force per unit area of adsorbed gas, m – adsorbed molecule mass, I? – detector site surface assimilation cross subdivision, Eb – adhering energy of the adsorbed molecule and I? is the oscillation frequence of the corresponding atom ( typically I? = 1012A Hz ).
5.4. Mold of the adsorption-desorption noise
In order to happen the depedence of the fluctuation I?N ( T ) around the value N0 at the adsorption-desorption equilibrium on the thickness of the feeling bed, little fluctuations of N around the value N0 are considered as done in [ 3 ] and [ 4 ]. After some computation processs, the undermentioned differential equation is obtained [ 4 ] :
( 16 )
where ( 17 )
In order to find the power spectral denseness of the adsorbed molecules denseness fluctuation, Wiener-Khinchin theorem [ 19 ] can be applied. The theorem states that spectral denseness of a wide-sense stationary random procedure ( sphere A is considered ) is the Fourier transform of the corresponding autocorrelation map. Since frequences can be merely positive in physical procedures, the above mentioned spectral denseness peers two times Fourier transform. Autocorrelation map is an even map, therefore, factor two is included once more, the power denseness spectrum of the adsorbed molecules denseness fluctuation writes [ 20 ] :
, ( 18 )
where I?2 denotes the mean square value of I?N.
As mentioned above, the experimental consequences of humidness measurings show that the concentration of detected affair affects the spectral denseness of frequence difference fluctuations. The low-frequency constituent ( 1/f noise ) changes insignificantly, while G-R constituent additions with a rise of concentration. Therefore, it can be assumed that a displacement of G-R noise is caused by increased flux denseness between the sorbent bed of QCM and the ambient environment. The increased flux of molecules corresponds to the increased fluctuation of frequence difference fluctuations. Relation ( 18 ) can be rewritten
, ( 19 )
where I?I”f 2 denotes the discrepancy of frequence difference fluctuations. On the footing of the theoretical account and experimental consequences ( frequence alteration and its 2nd statistical minute ), the clip I„ for molecule gaining control can be estimated. Refering the Fig.A 4 and the comparative humidness 30 % at frequence 2A Hz, the clip changeless peers to 1.26 Aµs and is calculated on the footing of parametric quantities estimated from the measuring, spectral denseness Si?„fA =A 7.26A xA 10-6 Hz2/s and standard divergence I?I”f = 1.21A Hz. For the comparative humidness 70 % at frequence 2A Hz, the clip changeless I„ = 1.23 Aµs is calculated from values Si?„f = 2.15 ten 10-5 Hz2/s and standard divergence I?I”f = 2.11 Hz.
Experimental consequences showed that soaking up of detected affair affects the frequence fluctuations. The paper focuses on adsorptionaˆ‘desorption noise without consideration of the diffusion procedure in an active bed, and presents its theoretical account, which is developed on the footing of the Kolmogorov equation for interaction between two reservoirs. The chance, that molecules will be captured on an active bed of the detector, is relative to the adsorbed molecule thermic speed and the surface site cross subdivision.
The chances, that surface sites are free or occupied by molecules, are implied by the Kolmogorov equation in the instance of thermodynamic equilibrium, when the flux of emitted atoms is the same as the flux of captured atoms on the active bed of the detector. The derived chance distributions are similar to the Fermi – Dirac statistics for semiconducting materials. The surface denseness of adsorbed molecules is relative to the surface site cross subdivision, adsorbed molecule thermic speed, concentration of adsorbed molecules and detector surface denseness of the sites. The adsorption-desorption dynamicss described by the Kolmogorov equation is compared with the Wolkenstein and Langmuir equations.
The ascertained comparative alterations of noise spectral denseness at different RH values correspond to the frequence displacement. Further, these alterations represent information, which can heighten selectivity and sensitiveness of the QCM detector. On the footing of the theoretical account and experimental consequences ( frequence alteration and its 2nd statistical minute ), the clip I„ for molecule gaining control can be estimated which can give extra information about procedures on the sorption beds. Therefore, we can reason that fluctuation enhanced noise feeling can be utilized for gas measurings by QCM detectors.
This research has been supported by the Czech Ministry of Education in the frame of MSM 0021630503 Research Intention MIKROSYN New Trends in Microelectronic System and Nanotechnologies, by undertaking MSM6046137306 and by the Grant Agency of Czech Republic undertakings No. 102/09/1920 and 108/11/1298.